The equation of a circle $C$ is $x^2+y^2+14x+14y+73 = 0$. What is its center $(h, k)$ and its radius $r$ ?
To find the equation in standard form, complete the square. $(x^2+14x) + (y^2+14y) = -73$ $(x^2+14x+49) + (y^2+14y+49) = -73 + 49 + 49$ $(x+7)^{2} + (y+7)^{2} = 25 = 5^2$ Thus, $(h, k) = (-7, -7)$ and $r = 5$.